(a) Distinguish the "T" (tense) and 'R' (relax) conformations of Hemoglobin on reversible binding of oxygen (O₂). 15 marks (b)…

(a) T and R states of haemoglobin. Haemoglobin reversibly interconverts between T (tense) and R (relaxed) quaternary conformations. In the T state, the Fe²⁺ ion of each deoxy haem is high-spin and sits slightly out of the porphyrin plane, displaced toward the proximal histidine; the α₁β₂ subunit interfaces contain stabilising salt bridges, and the O₂-binding pockets are constrained, so O₂ affinity is low. In the R state, O₂ binding converts Fe²⁺ to low-spin; the iron moves into the porphyrin plane, pulls the proximal histidine and F-helix, breaks the T-state salt bridges, and opens the quaternary structure. The R state therefore has high O₂ affinity. The key distinction is that the T state has an out-of-plane, constrained iron and low affinity, whereas the R state has an in-plane iron and high affinity. This T→R shift produces cooperative binding, with a Hill coefficient of about 2.8–3.0. Deoxygenation reverses the change, allowing the T state to re-form and O₂ to be released in tissues.

(b) Cytochrome b, cytochrome c and cytochrome c oxidase. Cytochrome b is an integral membrane protein of Complex III, the bc1 complex. It contains b-type hemes, usually bL and bH, in which protoporphyrin IX is non-covalently bound to the protein; it is a membrane-embedded electron-transfer centre involved in the Q cycle. Cytochrome c is a peripheral protein on the outer surface of the inner mitochondrial membrane. Its c-type heme is covalently attached to the protein through thioether bonds from cysteine residues to the porphyrin ring, and it acts as a mobile electron carrier between Complex III and Complex IV. The basic difference is therefore location and heme attachment: cytochrome b is integral and non-covalent, while cytochrome c is peripheral and covalent. Cytochrome c oxidase, Complex IV, is the terminal oxidase. It contains CuA, heme a, heme a₃ and CuB. It accepts electrons from reduced cytochrome c, transfers them to O₂, and catalyses the four-electron reduction of O₂ to H₂O. In doing so it pumps protons from the matrix to the intermembrane space, contributing to the proton-motive force used for ATP synthesis.

(c) Stereoisomers of the dinuclear cobalt complex. The printed ion is a dinuclear Co complex in which each Co is octahedrally coordinated by two en chelates and by the two bridging nitrogen donors, one from NO₂ and one from NH₂. Each metal centre is therefore locally of the [Co(en)₂B₂] type, where B denotes a bridging N donor. The two B donors at a Co can be cis or trans. In the drawn structure the NO₂ and NH₂ bridges are cis at both Co centres, giving a Co₂N₂ ring. For a cis [Co(en)₂B₂] unit, the two en chelates can be arranged as Δ or Λ; hence each Co centre is chiral. In the dimer the possible configurations are ΔΔ, ΛΛ and ΔΛ. The ΔΔ and ΛΛ forms are non-superimposable mirror images and are optically active. If the two en chelates at one Co are drawn as Δ and at the other as Λ, the bridging NO₂ and NH₂ groups can lie in a mirror plane, so the ΔΛ form is a meso form and is optically inactive. If a trans-bridged isomer is considered, in which the two B donors are opposite at each Co, the local [Co(en)₂B₂] unit possesses a plane of symmetry and is optically inactive. Thus optical activity is associated with the cis-bridged, homochiral ΔΔ/ΛΛ pair, while trans or heterochiral ΔΛ arrangements are inactive.

(d) Kinetics. For A + B → P, with initial concentrations a and b and x reacted after time t, the concentrations are (a−x) and (b−x). The rate is dx/dt = k₂(a−x)(b−x). Separating variables gives dx/[(a−x)(b−x)] = k₂ dt. Using partial fractions, 1/[(a−x)(b−x)] = 1/(a−b) [1/(b−x) − 1/(a−x)]. Integrating from x=0 to x and t=0 to t gives k₂t = 1/(a−b) {ln[(a−x)/(b−x)] − ln(a/b)} = 1/(a−b) ln [b(a−x)/a(b−x)]. Hence k₂ = 1/[(a−b)t] ln [b(a−x)/a(b−x)], valid for a > b. Since rate is mol dm⁻³ s⁻¹ and the concentration term is (mol dm⁻³)², the unit of k₂ is dm³ mol⁻¹ s⁻¹.

For a zeroth-order reaction, rate = k₀, so k₀ has the same unit as rate, mol dm⁻³ s⁻¹. For a reaction of order 5/2, rate = k C to the 5/2 power. The concentration factor is (mol dm⁻³) to the 5/2 power, i.e. mol to the 5/2 power and dm to the −15/2 power. Hence the unit of k is (mol dm⁻³ s⁻¹) divided by that concentration factor, giving dm⁴·⁵ mol⁻¹·⁵ s⁻¹, which is the same as dm to the 9/2 power, mol to the −3/2 power, and s to the −1 power.

(e) Reaction and π-bonding mechanism. The reaction is completed as: [PtCl₃(η²-C₂H₄)]⁻ + NH₃ → trans-[PtCl₂(NH₃)(η²-C₂H₄)] + Cl⁻, the major product having NH₃ trans to C₂H₄. The substitution is associative. NH₃ approaches the square-planar Pt(II) centre perpendicular to the ligand plane and forms a five-coordinate trigonal-bipyramidal intermediate, [PtCl₃(NH₃)(C₂H₄)]⁻. In this intermediate the entering NH₃ and the leaving Cl occupy the axial positions, while the three spectator ligands, C₂H₄ and the two remaining Cl, occupy equatorial positions. The chloride that leaves is the one originally trans to C₂H₄. This selectivity is explained by π-bonding theory: C₂H₄ donates its π electron pair to an empty Pt orbital and Pt back-donates from a filled dπ orbital into the C₂H₄ π* orbital. This π-acceptor interaction strengthens the Pt–C₂H₄ bond, stabilises the crowded five-coordinate intermediate, and weakens the Pt–Cl bond trans to C₂H₄ by drawing electron density from the d orbital involved in M–Cl bonding. Consequently the trans chloride is labilised, NH₃ replaces it, and the product retains the η²-ethylene ligand.

Together, these answers show how metal-centre geometry, chirality, electron transfer and π-bonding control function in bioinorganic and coordination chemistry: haemoglobin uses T/R switching for cooperative O₂ transport, cytochromes use heme type and location for electron transfer, and the Pt complex uses π-acceptor bonding to determine which ligand is substituted.